Local Laws of the Iterated Logarithm for Diffusions
Bass, R. F. ; Erickson, K. B.
Ann. Probab., Tome 13 (1985) no. 4, p. 616-624 / Harvested from Project Euclid
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Suppose $X_t$ is a diffusion, reflecting at 0, with speed measure $m(dx)$. We show, under a mild regularity condition on $m$, that $\lim\sup_{t\rightarrow 0} X_t/h^{-1}(t) = c$, a.s., where $c$ is a nonzero constant and $h(t) = tm\lbrack 0, t\rbrack/\log|\log t|$. The analogue to Chung's law of the iterated logarithm is also obtained.
Publié le : 1985-05-14
Classification:  Law of the iterated logarithm,  diffusions,  additive functionals,  speed measure,  Bessel process,  60J60,  60F15,  60J55 
@article{1176993014,
     author = {Bass, R. F. and Erickson, K. B.},
     title = {Local Laws of the Iterated Logarithm for Diffusions},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 616-624},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993014}
}

Bass, R. F.; Erickson, K. B. Local Laws of the Iterated Logarithm for Diffusions. Ann. Probab., Tome 13 (1985) no. 4, pp.  616-624. http://gdmltest.u-ga.fr/item/1176993014/